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Template background model production with Gammapy

Introduction

In this tutorial, we will create a template background model in the bkg_2d format, i.e. with offset and energy axes (see spec).

We will be working with only 4 H.E.S.S. runs on the Crab nebula here, just as an example.

To build a coherent background model you normally use 100s of runs of AGN observations or intentional “off” runs that point at parts of the sky containing no known gamma-ray sources.

We will mainly be using the following classes:

Setup

As always, we start the notebook with some setup and imports.

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
In [2]:
import shutil
import numpy as np
import astropy.units as u
from astropy.table import Table
from astropy.coordinates import SkyCoord, Angle
In [3]:
from gammapy.extern.pathlib import Path
from gammapy.utils.energy import EnergyBounds
from gammapy.utils.nddata import sqrt_space
from gammapy.data import DataStore, ObservationGroupAxis, ObservationGroups
from gammapy.background import EnergyOffsetBackgroundModel
from gammapy.background import OffDataBackgroundMaker
from gammapy.catalog import SourceCatalogGammaCat

Compute background model

Computing a set of template background model has two major steps: 1. Define group of runs for each background model 2. Run the OffDataBackgroundMaker

We also need a scratch directory, and a table of known gamma-ray sources to exclude.

Make a scratch directory

Background model production is a little pipeline that needs a “scratch” directory to put some files while running. Let’s make ourselves a fresh empty scratch sub-directory called background in the current working directory.

In [4]:
def make_fresh_dir(path):
    """Make a fresh directory. Delete first if exists"""
    path = Path(path)
    if path.is_dir():
        shutil.rmtree(str(path))
    path.mkdir()
    return path
In [5]:
scratch_dir = make_fresh_dir('background')
scratch_dir
Out[5]:
PosixPath('background')

Make an observation table defining the run grouping

Prepare a scheme to group observations with similar observing conditions and create a new ObservationTable with the grouping ID for each run

In [6]:
# Create a background model from the 4 Crab runs for the counts ouside the exclusion region so here outside the Crab
data_store = DataStore.from_dir("$GAMMAPY_EXTRA/datasets/hess-crab4-hd-hap-prod2")

# Define the grouping you want to use to group the obervations to make the acceptance curves
# Here we use 2 Zenith angle bins only, you can also add efficiency bins for example etc...
axes = [ObservationGroupAxis('ZEN_PNT', [0, 49, 90], fmt='edges')]

# Create the ObservationGroups object
obs_groups = ObservationGroups(axes)
# write it to file
filename = str(scratch_dir / 'group-def.fits')
obs_groups.obs_groups_table.write(filename, overwrite=True)

# Create a new ObservationTable with the column group_id
# You give the runs list you want to use to produce the background model that are in your obs table.
# Here very simple only the 4 Crab runs...
list_ids = [23523, 23526, 23559, 23592]
obs_table_with_group_id = obs_groups.apply(data_store.obs_table.select_obs_id(list_ids))

Make table of known gamma-ray sources to exclude

We need a mask to remove known sources from the observation. We use TeVcat and exclude a circular region of at least 0.3° radius. Here since we use Crab runs, we will remove the Crab events from the FOV to select only the OFF events to build the acceptance curves. Of cource normally you use thousand of AGN runs to build coherent acceptance curves.

In [7]:
cat = SourceCatalogGammaCat()
exclusion_table = cat.table.copy()
exclusion_table.rename_column('ra', 'RA')
exclusion_table.rename_column('dec', 'DEC')
radius = exclusion_table['morph_sigma'].data
radius[np.isnan(radius)] = 0.3
exclusion_table['Radius'] = radius * u.deg
exclusion_table = Table(exclusion_table)

Run the OffDataBackgroundMaker

Make the acceptance curves in the different group of observation conditions you defined above using the obs_table containaing the group id for each observation used to compute the bkg model

In [8]:
bgmaker = OffDataBackgroundMaker(
    data_store=data_store,
    outdir=str(scratch_dir),
    run_list=None,
    obs_table=obs_table_with_group_id,
    ntot_group=obs_groups.n_groups,
    excluded_sources=exclusion_table,
)

# Define the energy and offset binning to use
ebounds = EnergyBounds.equal_log_spacing(0.1, 100, 15, 'TeV')
offset = sqrt_space(start=0, stop=2.5, num=100) * u.deg

# Make the model (i.e. stack counts and livetime)
bgmaker.make_model("2D", ebounds=ebounds, offset=offset)

# Smooth the model
bgmaker.smooth_models("2D")

# Write the model to disk
bgmaker.save_models("2D")
bgmaker.save_models(modeltype="2D", smooth=True)

Congratulations, you have produced a background model.

The following files were generated in our scratch directory:

In [9]:
[path.name for path in scratch_dir.glob('*')]

Out[9]:
['background_2D_group_000_table.fits.gz',
 'background_2D_group_001_table.fits.gz',
 'group-def.fits',
 'smooth_background_2D_group_000_table.fits.gz',
 'smooth_background_2D_group_001_table.fits.gz']

Inspect the background model

Our template background model has two axes: offset and energy.

Let’s make a few plots to see what it looks like: 1. Acceptance curve (background rate as a function of field of view offset for a given energy) 1. Rate spectrum (background rate as a function of energy for a given offset) 1. Rate image (background rate as a function of energy and offset)

Acceptance curve

In [10]:
# Read one of the background models from file
filename = scratch_dir / 'smooth_background_2D_group_000_table.fits.gz'
model = EnergyOffsetBackgroundModel.read(str(filename))
In [11]:
offset = model.bg_rate.offset_bin_center
energies = model.bg_rate.energy
iE = 6

x = offset
y = model.bg_rate.data[iE,:]
plt.plot(x, y, label="bkg model smooth")
title = "energy band: "+str("%.2f"%energies[iE].value)+"-"+str("%.2f"%energies[iE+1].value)+" TeV"
plt.title(title)
plt.xlabel("Offset (degree)")
plt.ylabel("Bkg rate (MeV-1 s-1 sr-1)")
plt.legend()
Out[11]:
<matplotlib.legend.Legend at 0x10ee9ea58>
../_images/notebooks_background_model_19_1.png

Background rate spectrum

In [12]:
x = energies.log_centers
y = model.bg_rate.data[:,10]
plt.loglog(x, y, label="bkg model smooth")
plt.title("offset: "+str("%.2f"%offset[10].value)+" deg")
plt.xlabel("Energy (TeV)")
plt.ylabel("Bkg rate (MeV-1 s-1 sr-1)")
Out[12]:
<matplotlib.text.Text at 0x10f13f940>
../_images/notebooks_background_model_21_1.png

Background rate image with energy and offset axes

It doesn’t look good in this case. To do this well, you need to use more off or AGN runs to build the background model!

In [13]:
model.bg_rate.plot()
Out[13]:
<matplotlib.axes._subplots.AxesSubplot at 0x10f241dd8>
../_images/notebooks_background_model_23_1.png

Make new HDU index table including background

Here we first copy the dataset of the 4 crab runs from gammapy-extra in a new directory containing the data you will use for the analysis.

We use the same dataset to produce the bkg or for the analysis. Of course normally you produce the bkg model using thousands of AGN runs not the 4 Crab test runs.

In [14]:
# Make a new hdu table in your dataset directory that contains the link to the acceptance curve to use to build the bkg model in your cube analysis
data_dir = make_fresh_dir('data')
In [15]:
ds = DataStore.from_dir("$GAMMAPY_EXTRA/datasets/hess-crab4-hd-hap-prod2")
ds.copy_obs(ds.obs_table, data_dir)

The hdu_table in this directory contains no link to a bkg model for each observation.

In [16]:
data_store = DataStore.from_dir(data_dir)
data_store.hdu_table
Out[16]:
<HDUIndexTable length=28>
OBS_IDHDU_TYPEHDU_CLASSFILE_DIRFILE_NAMEHDU_NAMESIZEMTIMEMD5
int64str6str10str26str30str12int64float64str32
23523gtigtirun023400-023599/run023523hess_events_023523.fits.gzGTI6209751455089616.349e402094c3a3e05ae4199b7cc9a01215
23523eventseventsrun023400-023599/run023523hess_events_023523.fits.gzEVENTS6209751455089616.349e402094c3a3e05ae4199b7cc9a01215
23523aeffaeff_2drun023400-023599/run023523hess_aeff_2d_023523.fits.gzAEFF_2D37271455089616.346430c082176f092e0aed0f2bf9840915
23523edispedisp_2drun023400-023599/run023523hess_edisp_2d_023523.fits.gzEDISP_2D289631455089616.34f580ea6cb104e4d6735b8d2940ac6774
23523psfpsf_3gaussrun023400-023599/run023523hess_psf_3gauss_023523.fits.gzPSF_2D_GAUSS30271455089616.3487f2d5c5ca56575a4a083b33e9700312
23523psfpsf_kingrun023400-023599/run023523hess_psf_king_023523.fits.gzPSF_2D_KING18231455089616.347760e349a40883345406c7e3ea1cbd54
23523psfpsf_tablerun023400-023599/run023523hess_psf_table_023523.fits.gzPSF_2D_TABLE2215741455089616.3574b745938341d0f64b79f60da7f1ad0f
23526psfpsf_kingrun023400-023599/run023526hess_psf_king_023526.fits.gzPSF_2D_KING18341455089616.565873e4ec0771bdfcc6d82608199a4067
23526psfpsf_3gaussrun023400-023599/run023526hess_psf_3gauss_023526.fits.gzPSF_2D_GAUSS30021455089616.56f27364b40bbf8e35c747828e60224b28
23526edispedisp_2drun023400-023599/run023526hess_edisp_2d_023526.fits.gzEDISP_2D288821455089616.56c7e99f4d282a55c7fdd4024167bdbef5
...........................
23559eventseventsrun023400-023599/run023559hess_events_023559.fits.gzEVENTS6205771455089616.77311bd2ede3dddb3504c11b9c3dadac32
23559gtigtirun023400-023599/run023559hess_events_023559.fits.gzGTI6205771455089616.77311bd2ede3dddb3504c11b9c3dadac32
23559aeffaeff_2drun023400-023599/run023559hess_aeff_2d_023559.fits.gzAEFF_2D37151455089616.7850eb94ec65ac146ff60845860d84a1a2
23592psfpsf_kingrun023400-023599/run023592hess_psf_king_023592.fits.gzPSF_2D_KING18181455089617.0514f94397507d1160341387ed56e80ba
23592gtigtirun023400-023599/run023592hess_events_023592.fits.gzGTI5981071455089616.993c94433be8e9f29aa198065403570dbb
23592eventseventsrun023400-023599/run023592hess_events_023592.fits.gzEVENTS5981071455089616.993c94433be8e9f29aa198065403570dbb
23592aeffaeff_2drun023400-023599/run023592hess_aeff_2d_023592.fits.gzAEFF_2D37211455089616.995e2f5dc70fecb5060b6e1662d59d9507
23592edispedisp_2drun023400-023599/run023592hess_edisp_2d_023592.fits.gzEDISP_2D289311455089616.9937db40409b6c37a9060aef8817a14ffe
23592psfpsf_3gaussrun023400-023599/run023592hess_psf_3gauss_023592.fits.gzPSF_2D_GAUSS30151455089617.03763f28acd61d96724ad5584fe1f39c4
23592psfpsf_tablerun023400-023599/run023592hess_psf_table_023592.fits.gzPSF_2D_TABLE2217091455089617.038be05a13aa0bd492c9979c5b7d3d47f

In order to produce a background image or background cube we have to create a hdu table that contains for each observation a link to the bkg model to use depending of the observation conditions of the run.

In [17]:
#Copy the background directory in the one where is located the hdu table, here data
shutil.move(str(scratch_dir), str(data_dir))

# Create the new hdu table with a link to the background model
group_filename = data_dir / 'background/group-def.fits'

#relat_path= (scratch_dir.absolute()).relative_to(data_dir.absolute())
hdu_index_table = bgmaker.make_total_index_table(
    data_store=data_store,
    modeltype='2D',
    out_dir_background_model=scratch_dir,
    filename_obs_group_table=str(group_filename),
    smooth=False,
)

# Write the new hdu table
filename = data_dir / 'hdu-index.fits.gz'
hdu_index_table.write(str(filename), overwrite=True)
In [18]:
hdu_index_table
Out[18]:
<HDUIndexTable masked=True length=32>
OBS_IDHDU_TYPEHDU_CLASSFILE_DIRFILE_NAMEHDU_NAMESIZEMTIMEMD5
int64str6str10str26str37str12int64float64str32
23523gtigtirun023400-023599/run023523hess_events_023523.fits.gzGTI6209751455089616.349e402094c3a3e05ae4199b7cc9a01215
23523eventseventsrun023400-023599/run023523hess_events_023523.fits.gzEVENTS6209751455089616.349e402094c3a3e05ae4199b7cc9a01215
23523aeffaeff_2drun023400-023599/run023523hess_aeff_2d_023523.fits.gzAEFF_2D37271455089616.346430c082176f092e0aed0f2bf9840915
23523edispedisp_2drun023400-023599/run023523hess_edisp_2d_023523.fits.gzEDISP_2D289631455089616.34f580ea6cb104e4d6735b8d2940ac6774
23523psfpsf_3gaussrun023400-023599/run023523hess_psf_3gauss_023523.fits.gzPSF_2D_GAUSS30271455089616.3487f2d5c5ca56575a4a083b33e9700312
23523psfpsf_kingrun023400-023599/run023523hess_psf_king_023523.fits.gzPSF_2D_KING18231455089616.347760e349a40883345406c7e3ea1cbd54
23523psfpsf_tablerun023400-023599/run023523hess_psf_table_023523.fits.gzPSF_2D_TABLE2215741455089616.3574b745938341d0f64b79f60da7f1ad0f
23526psfpsf_kingrun023400-023599/run023526hess_psf_king_023526.fits.gzPSF_2D_KING18341455089616.565873e4ec0771bdfcc6d82608199a4067
23526psfpsf_3gaussrun023400-023599/run023526hess_psf_3gauss_023526.fits.gzPSF_2D_GAUSS30021455089616.56f27364b40bbf8e35c747828e60224b28
23526edispedisp_2drun023400-023599/run023526hess_edisp_2d_023526.fits.gzEDISP_2D288821455089616.56c7e99f4d282a55c7fdd4024167bdbef5
...........................
23592gtigtirun023400-023599/run023592hess_events_023592.fits.gzGTI5981071455089616.993c94433be8e9f29aa198065403570dbb
23592eventseventsrun023400-023599/run023592hess_events_023592.fits.gzEVENTS5981071455089616.993c94433be8e9f29aa198065403570dbb
23592aeffaeff_2drun023400-023599/run023592hess_aeff_2d_023592.fits.gzAEFF_2D37211455089616.995e2f5dc70fecb5060b6e1662d59d9507
23592edispedisp_2drun023400-023599/run023592hess_edisp_2d_023592.fits.gzEDISP_2D289311455089616.9937db40409b6c37a9060aef8817a14ffe
23592psfpsf_3gaussrun023400-023599/run023592hess_psf_3gauss_023592.fits.gzPSF_2D_GAUSS30151455089617.03763f28acd61d96724ad5584fe1f39c4
23592psfpsf_tablerun023400-023599/run023592hess_psf_table_023592.fits.gzPSF_2D_TABLE2217091455089617.038be05a13aa0bd492c9979c5b7d3d47f
23526bkgbkg_2dbackgroundbackground_2D_group_000_table.fits.gzbkg_2d------
23559bkgbkg_2dbackgroundbackground_2D_group_000_table.fits.gzbkg_2d------
23592bkgbkg_2dbackgroundbackground_2D_group_000_table.fits.gzbkg_2d------
23523bkgbkg_2dbackgroundbackground_2D_group_001_table.fits.gzbkg_2d------
In [19]:
print(hdu_index_table[-4]["FILE_DIR"], " ", hdu_index_table[-4]["FILE_NAME"])
background   background_2D_group_000_table.fits.gz
In [20]:
print(hdu_index_table[-1]["FILE_DIR"], " ", hdu_index_table[-1]["FILE_NAME"])
background   background_2D_group_001_table.fits.gz

Exercises

  • Use real AGN run
  • Change the binning for the grouping: thinner zenithal bin, add efficiency binning ….
  • Change the energy binning (ebounds) and the offset (offset) used to compute the acceptance curve

What next?

In this tutorial we have created a template background model in the bkg_2d format, i.e. with offset and energy axes (see spec).

In future tutorials, we will use this background model as one of the model components for source analysis.